Finite Group Databasebeta

← Group #323992

Character table — Group #323992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888824444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1111111111111-1-11111-1-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-11
χ9111111111111111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1
χ10111111111111111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ12111111111111111111-1-1-1-111111111-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1111111111111-1-11-11-1
χ1722222222222-2-2-2-22-2-222-2-22222-2-2-2-2-200000020022000000000000-2-2000000000000
χ1822222222222-2-2-2-22-2-222-2-2-2-2-2-22222-2000000200-2-200000000000022000000000000
χ1922222222222-2-2-2-22-2-2-2-2222222-2-2-2-22000000-200-2-200000000000022000000000000
χ2022222222222-2-2-2-22-2-2-2-222-2-2-2-222222000000-20022000000000000-2-2000000000000
χ2122222222-2-2-22222-2-2-2222200000000-22222-2-2-2-2-20000000000000000000000000000
χ2222222222-2-2-22222-2-2-2222200000000-2-2-2-2-222-2220000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-200000000222-2-2222-2-20000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2000000002-2-222-2-22220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000002000000-200002i2i−2i−2i00000000002i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2000000002000000-20000−2i−2i2i2i0000000000−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000-2000000200002i2i−2i−2i0000000000−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000-200000020000−2i−2i2i2i00000000002i2i−2i−2i00000000
χ2922-2-22-2-2200022-2-20002i−2i2i−2i22−2−222−2−2000002i−2i02-2i2−i2i2−i2i2−i200000000i2−i22−22−200000000
χ3022-2-22-2-2200022-2-20002i−2i2i−2i22−2−222−2−200000−2i2i0-22i2−i2−i2i2−i2i200000000i2−i2−22−2200000000
χ3122-2-22-2-2200022-2-20002i−2i2i−2i−2−222−2−222000002i−2i02-2−i2i2−i2i2−i2i200000000−i2i2−22−2200000000
χ3222-2-22-2-2200022-2-20002i−2i2i−2i−2−222−2−22200000−2i2i0-22−i2i2i2−i2i2−i200000000−i2i22−22−200000000
χ3322-2-22-2-2200022-2-2000−2i2i−2i2i22−2−222−2−2000002i−2i0-22−i2i2i2−i2i2−i200000000−i2i2−22−2200000000
χ3422-2-22-2-2200022-2-2000−2i2i−2i2i22−2−222−2−200000−2i2i02-2−i2i2−i2i2−i2i200000000−i2i22−22−200000000
χ3522-2-22-2-2200022-2-2000−2i2i−2i2i−2−222−2−222000002i−2i0-22i2−i2−i2i2−i2i200000000i2−i22−22−200000000
χ3622-2-22-2-2200022-2-2000−2i2i−2i2i−2−222−2−22200000−2i2i02-2i2−i2i2−i2i2−i200000000i2−i2−22−2200000000
χ3722-2-22-2-22000-2-2220002i−2i−2i2i22−2−2−2−22202i−2i2-200000i2−i22−2−2200000000−i2i2−i2i2i2−i200000000
χ3822-2-22-2-22000-2-2220002i−2i−2i2i22−2−2−2−2220−2i2i-2200000i2−i2−222−200000000−i2i2i2−i2−i2i200000000
χ3922-2-22-2-22000-2-2220002i−2i−2i2i−2−22222−2−202i−2i2-200000−i2i2−222−200000000i2−i2i2−i2−i2i200000000
χ4022-2-22-2-22000-2-2220002i−2i−2i2i−2−22222−2−20−2i2i-2200000−i2i22−2−2200000000i2−i2−i2i2i2−i200000000
χ4122-2-22-2-22000-2-222000−2i2i2i−2i22−2−2−2−22202i−2i-2200000−i2i2−222−200000000i2−i2−i2i2i2−i200000000
χ4222-2-22-2-22000-2-222000−2i2i2i−2i22−2−2−2−2220−2i2i2-200000−i2i22−2−2200000000i2−i2i2−i2−i2i200000000
χ4322-2-22-2-22000-2-222000−2i2i2i−2i−2−22222−2−202i−2i-2200000i2−i22−2−2200000000−i2i2i2−i2−i2i200000000
χ4422-2-22-2-22000-2-222000−2i2i2i−2i−2−22222−2−20−2i2i2-200000i2−i2−222−200000000−i2i2−i2i2i2−i200000000
χ452-2-22-22-2222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000022-2-2000000002i−2i0000
χ462-2-22-22-2222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000-2-22200000000−2i2i0000
χ472-2-22-22-2222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000022-2-200000000−2i2i0000
χ482-2-22-22-2222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000-2-222000000002i−2i0000
χ492-2-22-22-2222-2-22-22-2-2200002i−2i2i−2i−2i2i−2i2i00000000000000002i2i−2i−2i00000000002-2000000
χ502-2-22-22-2222-2-22-22-2-2200002i−2i2i−2i−2i2i−2i2i0000000000000000−2i−2i2i2i0000000000-22000000
χ512-2-22-22-2222-2-22-22-2-220000−2i2i−2i2i2i−2i2i−2i00000000000000002i2i−2i−2i0000000000-22000000
χ522-2-22-22-2222-2-22-22-2-220000−2i2i−2i2i2i−2i2i−2i0000000000000000−2i−2i2i2i00000000002-2000000
χ53444-4-44-4-44-4-40000400000000000000000000000000000022−2222−22000000000000000000
χ54444-4-44-4-44-4-400004000000000000000000000000000000−2222−2222000000000000000000
χ55444-4-44-4-4-4440000-4000000000000000000000000000000000022−2222−2200000000000000
χ56444-4-44-4-4-4440000-40000000000000000000000000000000000−2222−222200000000000000
χ574-44-4-4-4440004-4-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ584-44-4-4-4440004-4-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-44-4-4-444000-444-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ604-44-4-4-444000-444-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ614-4-44-44-44-4-444-44-44-4400000000000000000000000000000000000000000000000000
χ624-4-44-44-44-4-44-44-4444-400000000000000000000000000000000000000000000000000
χ634-4-4-4444-44-440000-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ644-4-4-4444-44-440000-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ654-4-4-4444-4-44-400004000000000000000000000000000000000022−22−222200000000000000
χ664-4-4-4444-4-44-4000040000000000000000000000000000000000−222222−2200000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).